This BE speaker isn't very keen on the plural form in this particular sentence.
Would I be right to assume that this is a teacher who wants to get their students to play around with words, making puns perhaps?
Let's try some wordplay.
Let's try to invent some puns.
Let's try to make plays on words.
1. Let’s try to create plays on words.
2. Let’s try to make plays on words.
I agree with #4. In AE both sentences sound very awkward (though they may be "correct grammar"). The sentences are missing an article. Where "a" and "the" are used for singular nouns, "some" is used for plural nouns (or "any" in some situations like questions). All of these sound better in AE:
3. Let's try to create some plays on words.
4. Let's try to make some plays on words.
5. Let's try to think up some plays on words.
In AE, I like 5 the best, then 3, then 4.
Using "make" (sentences 2 and 4) is a bit confusing because "make a play on" is a standard idiom, so 4 might mean either: